In this section, we revisit the OFDM-based implementation of OTFS usually used in the literature. In the OFDM implementation, OTFS is considered as an additional pre- and post-processing, given by the ISFFT and SFFT. OTFS literature typically considers pulse shaping OFDM (see for example [1]}, [2]}, [3]}), i.e., transmit and receive pulses that are not necessarily rectangular. We consider the discrete version of pulse shaping OFDM [4]}. In this discrete setting, we consider all sequences, including the transmit and receive pulses, to be \(KL\) -periodic. Based on the discrete formulation, we will show that the overlay technique resembles the IDZT/DZT. We further show that the transmitted symbols can be recovered if the transmit and receive pulses satisfy the so-called biorthogonality condition.
